ENTHALPY-BASED DISTILLATION MODELING

PONCHON-SAVARITT ANALYSIS

PONCHON-SAVARIT ANALYSIS

• ENTHALPY CONCENTRATION EQUILIBRIUM DIAGRAM – POINTS REPRESENT CONCENTRATION, x

OR y, AND ENTHALPY, Hy OR hx.

– ANALYSIS INCLUDES CHANGES IN V/L AS A FUNCTION OF ΔHvap.

ENTHALPY EQUILIBRIUM DIAGRAM

http://www.hyper-tvt.ethz.ch/images/enthalpy.jpg

FORM OF SIMULATION DIAGRAM

XB XF XD

HB

HD

HF

H’D

H’B

-qC/D

qr/D

Hy1

x,y

HSATURATED VAPOR LINE

SATURATED LIQUID LINE

EQUILIBRIUM TIE LINES

ENTHALPY CONCENTRATION

COORDINATE SYSTEM

From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968

ENTHALPY CONCENTRATION RECTIFICATION

SECTION

From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968

ENTHALPY CONCENTRATION

STRIPPING SECTION

From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968

OPTIONS

• DATA FOR MIXTURE VALUES NOT READILY AVAILABLE

• CAN ASSUME IDEAL MIXTURES AND USE PURE COMPONENT DATA AT TERMINAL POINTS - THEN CONNECT WITH STRAIGHT LINE.

• EQULIBRIUM TIE LINES, LINK EQUILIBRIUM LIQUID & VAPOR CONCENTRATIONS ON EACH ENTHALPY LINE. SHOWN AS DASHED LINES FIG 11.6-1

SIMPLIFIED P-S DIAGRAM

XB XF XD

HB

HD

HF

H’D

H’B

-qC/D

qr/D

Hy1

x,y

H

SATURATED VAPOR LINE

SATURATED LIQUID LINE

EQUILIBRIUM TIE LINES

ENTHALPY BALANCES

• OVERALL

• CONDENSERB

qHH

D

qHH

BHDHFhBDF

rBB

cDD

BDF

''

''

Dnnnn DxxLyV 11

DLV nn 1

CDnLn

nVn

qDHHL

HV

,

1,1

CONSTRUCTION FOR GRAPHICAL MODEL

• ENTHALPY RIGOROUS EQUATION OR DATA

• SIMPLIFIED VERSION

• EQUILIBRIUM DATA

FROM VLE DATA

H kJ/mol

V

L

T1T2

T3T4

T5x1 x2 x3x4

x5

y1 y2y3

y4y5

)]()[1()]([

)()1()(

00

00

TTcyTTcyH

HTTcxTTcxh

PvBBAPvAAA

SOLNPlBAPlAA

BABA

BBAA

BBAA

HHhh

HHHyH

hhhxh

)(

)(

EQUILIBRIUM DATA TRANSFER

H kJ/mol

A

V

L

T1T2

T3T4

T5x1x2 x3x4

x5

y1 y2 y3 y4 y5

Tb(B)T

xA=1

Tb(A)

V

L

xA=0

T5T4T3T2T1

REBOILER HEAT BALANCE

• REBOILER

• OVERALL

Brmmmm BhqhBVHV )( 111

cFBDr qFhBhDhq

LOCATION OF FEED LINE• BASED ON FEED CONC. &

ENTHALPY - RELATIVE TO q VALUES ON McCABE-THEILE– SAT'D LIQ., q = 1, ON SAT'D LIQ.

ENTHALPY LINE– SAT'D VAPOR, q = 0, SAT'D VAP.

ENTHALPY LINE– PARTIAL SAT'D VAPOR, 0 < q < 1,

BETWEEN SAT'D ENTHALPY LINES WITH CONCENTRATION IN EACH PHASE BASED ON EQUILIBRIUM TIE LINES.

– SUPERCOOLED LIQ, q > 1, BELOW SAT'D LIQ. ENTHALPY LINE AT xF.

– SUPERHEATED VAP., q < 1, ABOVE SAT'D VAP. ENTHALPY LINE AT xF

x

V

Lq=0

q=1

q<1

q>1

0<q<1

COMPLETION OF DIAGRAM• FEED POINT, POINTS H’D

AND H’B LIE ON A COMMON LINE TO CLOSE THE ENTHALPY BALANCE

• PRODUCT ENTHALPIES– LOCATION OF H'D IS

BASED ON REFLUX RATIO:

– LOCATION OF H’B IS BASED ON BOILUP RATIO

H kJ/mol

x

V

L

H’B

xF xD

H’D

xBDy

yDad HH

HH

D

LR

1

1'

Byb

BBbB HH

HH

B

VR

'

LIMITING CASES• TOTAL REFLUX

– CONSTRUCTION HAS STEPS THAT ASSUME H’D IS LOCATED AT ∞ SO VERTICAL OPERATING LINES

– START AT ONE PRODUCT AND GO TO THE OTHER– RED LINES FOLLOW EQUILIBRIUM VALUES

x

V

L

H kJ/mol

xDxB

LIMITING CASES• INFINITE STAGES - RdMIN,

– LINE THROUGH FEED POINT FOLLOWS EQULIBRIUM LINE

– INTERSECTS WITH H’DMIN AT VERTICAL EXTENSION THROUGH PRODUCT CONCENTRATION

H kJ/mol

x

V

L

H’BMIN

xF xD

H’DMIN

xB

Dy

yDMINdMIN HH

HHR

1

1'

ACTUAL NUMBER OF STAGES

• RdDZN > RdMIN SO H’D > H’Dmin

• CONSTRUCTION PASSES THROUGH H’D AND H’B– STAGES ARE CALCULATED ABOVE &

BELOW FEED H kJ/mol

x

V

L

H’B

xF xD

H’D

xB

H kJ/mol

x

V

L

H’B

xF xD

H’D

xB

COMPARISON WITH M-T• P-S ANALYSIS CAN BE

TRANSFERRED TO M-C– OPERATING LINE IS

ADJUSTED TO ALLOW FOR CHANGES IN ΔHvap

– RESULTING NUMBER OF STAGES CAN DIFFER FROM STRAIGHT OPERATING LINE CALCULATIONS

• SEE FIGURE 11.6-3 FOR EXAMPLE

– M-T EQUILIBRIUM LINES ARE VERTICAL

– LINES AND POINTS ARE INTERCHANGED BETWEEN THE TWO METHODS.

ACTUAL STAGE COUNT FACTORS

• INTERSECTIONS OF OPERATING LINE WITH ENTHALPY LINES REPRESENT ACTUAL STAGE CONCENTRATIONS

• EQUILIBRIUM CONCENTRATIONS ON EACH STAGE ARE REPRESENTED BY EQUILIBRIUM TIE LINES

• MURPHREE EFFICIENCY– STAGE TO STAGE CONSTRUCTION IS

ADJUSTED SO THE ACTUAL CONCENTRATION CHANGE IS A FRACTION OF THE IDEAL

ADDITIONAL DESIGN FACTORS

• FEED LOCATION– IDEAL LOCATION IS ON A TRAY WHERE:

• TRAY CONCENTRATION = FEED CONCENTRATON

• FEED TEMP = SATURATION TEMP

– DEVIATIONS FROM THIS EQUALITY RESULTS IN SOME LOSS IN EFFICIENCY

• IT IS MINOR • IS INEVITABLE

TRAY DESIGN• COMPONENTS

– TRAYS– DOWNCOMERS– SUPPORTS

• TYPES - USED FOR GAS LIQUID CONTACTING– CAP– VALVES– SIEVES

Douglas L. Bennett and Kenneth W. Kovak, Optimize Distillation Columns, Chemical Engineering Progress, May 2000

TRAY HYDRODYNAMICS• PRESSURE DROPS (ENERGY LOSSES)AFFECT

EQUILIBRIUM AND SYSTEM ENERGY DEMANDS• LIQUID ΔP

– COMPENSATED BY GRAVITY– FRICTION LOSSES

• THROUGH DOWNCOMER• UNDER DOWNCOMER• OVER DOWNCOMER

– INERTIAL LOSS - CHANGE IN FLOW DIRECTION ON TRAY

– CONTRACTION/EXPANSION LOSSES DUE TO CHANGE IN FLOW CROSS-SECTION AREA

– EDDY LOSSES• AT WALLS• AT CAPS OR VALVES

TRAY HYDRODYNAMICS• VAPOR ΔP IS ALL THAT IS NORMALLY

CONSIDERED:

• hLIQUID HEAD

– BASED ON LIQUID LEVEL ON TRAY– RELATED TO RESIDENCE TIME OF THE

BUBBLE IN THE LIQUID – BASED ON WEIR HEIGHT LEVEL PLUS

HEIGHT OF LIQUID FLOW OVER WEIR

h h h HEAD LIQUIDORIFICETOTAL

IGHTOVERFLOWHEWEIRHEIGHTLIQUIDHEAD hhh

CORRELATION EQUATIONS• FLOW OVER A WEIR (FRANCIS EQN.)

• ORIFICE DROP– SIEVE TRAYS

323

443

/

)(

min)/(.)(

mL

mqmmh

W

LHEIGHTOVERFLOW

AREADOWNCOMERA

AREAPLATETOTALAAAAREAPLATEACTIVEA

AREAHOLEPLATETOTALACOEFFICENTORIFICEC

A

A

C

smuliqmmh

d

da

OO

a

O

L

V

O

OORIFICE

2

1512

2

2

,

)/()(

CORRELATION EQUATIONS

• BUBBLE CAPS ARE OF THE FORM

• VALVE TRAYS HAVE SIMILAR FORMS– SEE PERRY’S Pp. 14-11 THROUGH 14-38

FOR TRAYS AND 14-38 – THROUGH 14-58 FOR PACKING

VELOCITYVAPORMAXIMUMU

CONSTANTNCORRELATIOK

UKh

VC

C

L

VVCCBC

2

LIQUID-IN-VAPOR ENTRAINMENT

• CONTROLLED THROUGH DESIGN OF:– TRAY SPACING– VAPOR VELOCITY– LIQUID HEIGHT– VAPOR DENSITY– LIQUID SURFACE TENSION– HOLE DIAMETER

• VAPOR-IN-LIQUID ENTRAINMENT (FOAMING) CAN RESULT IN VAPOR BEING CARRIED DOWN THE THE LOWER TRAYS OR LIQUID AS BUBBLES BEING CARRIED TO THE TRAY ABOVE

TRAY EFFICIENCY

• CONTROLLING VARIABLES:– PATH LENGTH– BACKMIXING – BUBBLE FORMATION MECHANISM AND

PHASE CONTACT• ORIFICE SIZE• FREE AREA FOR BUBBLING

– RELATIVE VAPOR/LIQUID RATES

CORRELATIONS OF EMPIRICAL DATA

• USE PECLET NUMBER

– AIChE STANDARD METHOD (1958) FOR BUBBLE CAPS– GENERAL DIMENSIONLESS FORM USES AS POSSIBLE

VARIABLES: • VAPOR & LIQUID DENSITY, VISCOSITY AND DIFFUSIVITY• LIQUID SURFACE TENSION

– GENERAL FORM– ≈ + 12% ACCURACY

TRAYONTIMERESIDENCELIQUIDtYDIFFUSIVITEDDYD

PATHFLOWOFLENGTHZtD

ZPe

LE

LLE

L

2

EC

LL

L

B

vLM Du

A

SUMMARY OF COLUMN DESIGN• COLUMN

– OPERATING PRESSURE AND TEMPERATURE– REFLUX RATIO– NUMBER OF TRAYS– FEED AND DRAW-OFF LOCATIONS– COLUMN DIAMETER– TRAY SPACING

• TRAY– TYPE AND ARRANGEMENT– ACTIVE AREA– DOWNCOMER TYPE, AREA & CLEARANCE– MATERIALS OF CONSTRUCTION